Stability and bifurcation of prey-predator model with disease in prey incorporating anti-predator and hunting cooperation

This study's main goal is to determine how the prey population's cooperation and anti-predator behavior affect the prey-predator model's dynamic with disease in prey with the fear interaction. For this purpose, a mathematical model with Holling type II functional response was proposed and analyzed. The existence conditions of the equilibrium points with their stability analysis were analyzed to determine the qualitative behavior of the model. Numerical simulations are performed to support our analytical results. It is obtained that fear has a stabilizing role, whereas hunting cooperation has a destabilizing role in the system dynamics. Periodic oscillations were observed in the model through bifurcation.